Obscurity factor: 3
The war years had quite an impact on the film industry. Studios retooled, just as factories did, only instead of turning out planes and tanks, they turned out propaganda, training films and projects designed to keep the moral up. Disney's studio was no different. Because of a reduction in development staff they turned to projects like this, which utilized content they already had on the boards.
After You've Gone is the second Benny Goodman piece to be featured in the film. You'll see shades of Peter Max and other contemporary animation and illustration styles in this one. Look for the dancing fingers. It was uploaded by epcot
Here's The Martins and the Coys, the segment stripped from the home video releases of the film. It tells a Romeo and Juliet like story of star crossed lovers. It's uploade by 2wingo
The Andrews Sisters provided the song for this addition to the film. It tells the story of a hat who falls in love with a bonnet, but they are separated when different customers buy them.
The other Benny Goodman segment is All The Cats Join In and is very clever in its animation with everything originating from the point of the animator's pencil. This segment above is uploaded by Uncutcartoons247. The film is also the origin of the Disney version of Peter and the Wolf, which was shown to many elementary school students over the years, and The Whale who Wanted to Sing at the Met, voiced by Nelson Eddy.
The entire film is available on DVD in Disney's Gold Classic Collection, minus the hillbilly segment. You can also find many of the segments on YouTube separately.
Obscurity factor: 3 (available on DVD and in pieces on YouTube, known to Disney fans, relatively unknown otherwise)